Lightroom won't allow me to log in unless I have internet access

Ah, that would explain things then

Adding to what was previously stated. As a test, and a learning experiment,

with internet access, sign in using the Adobe Creative Cloud Desktop application. And as stated, do not sign out. Now if your computer only gets internet thru an ethernet cable, disconnect it, if you use WiFi, disable it. reboot your computer. Now no internet access, but lightroom still works, correct? Unless you go some 90 plus days without internet, lightroom should still work.

Next, sign out, reboot, retry, no lightroom, probably, reconnect internet, sign in, lightroom back.

upshot is to never sign out.

As above LR does not require an internet connection except if you haven't opened it for a period of time.

And even if you haven't opened it for an extended period of time, something around 90 days, it shouldn't ask you to sign in. it would just give you limited function.

That is unless you manually Sign out.

There is no good reason to Sign Out of LR when you are not using it.

Make sure you do not Log out or Sign out when you close the Lr application or shut down your computer since that will deactivate the application and you will have to sign in with internet access.

Do use the menu, click Lightroom at the top left of the application and click on Quit Lightroom from the pop up.